Finite Group Databasebeta

← #11771098

Subgroups — #11771098

Order 1152.

587 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 587 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592906C211yesmaximal, characteristic
2C3×C4×#217C212yesmaximal
3#67618—32nomaximal
4C23×C32×C4C2211yescharacteristic
5C2×#3748C412yescomplemented
6C2×C3×#217—22no—
7C2×C3×C4×Dic3—22no—
8#63657—22no—
9C3×C3⋊#95C414yescomplemented
10C3×C4×C22⋊C4—32no—
11C4×#217D312yes—
12#5207—32no—
13#5207—61no—
14C24×C32D411yescharacteristic
15C22×C32×C4—42no—
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4C2×C412yes—
18C22×C32×C4D412yes—
19C22×C32×C4Q811yescharacteristic
20C22×C3×Dic3—24no—
21#3748—42no—
22C2×C3⋊(C3⋊C8)—22no—
23C3×#217—28no—
24C3×C4×Dic3—44no—
25#1297—91noSylow
26C23×C3×C4—21no—
27C23×C3×C4C2×D312yes—
28C2×C3×C22⋊C4—62no—
29C2×C3×C42—62no—
30C2×#217—22no—
31C2×C4×Dic3—22no—
32C2×#208—34no—
33C2×#208—62no—
34C3×#95—34no—
35C3⋊#95Dic314yescomplemented
36#830—64no—
37#830—62no—
38#830—62no—
39C23×C32—24no—
40C23×C32—41no—
41C23×C32C22⋊C412yes—
42C23×C32C4⋊C411yescharacteristic
43C2×C32×C4—22no—
44C2×C32×C4—24no—
45C2×C32×C4—42no—
46C2×C32×C4—41no—
47C2×C32×C4C4211yescharacteristic
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C4⋊C412yes—
50C2×C3×Dic3—28no—
51C2×C3×Dic3—44no—
52C2×C3×Dic3—44no—
53C3⋊(C3⋊C8)—42no—
54#407—91no—
55C4×C22⋊C4—32no—
56C24×C3—21no—
57C24×C3#6712yes—
58C22×C3×C4—22no—
59C22×C3×C4—21no—
60C22×C3×C4—22no—
61C22×C3×C4—21no—
62C22×C3×C4—44no—
63C22×C3×C4—44no—
64C22×C3×C4—64no—
65C22×C3×C4Dic612yes—
66C22×C3×C4C4×D312yes—
67C22×C3×C4C4×D312yes—
68C22×C3×C4D1212yes—
69C22×C3×C4C2×Dic312yes—
70C22×C3×C4#6712yes—
71C22×Dic3—24no—
72C3×C22⋊C4—68no—
73C3×C42—124no—
74#217—28no—
75C4×Dic3—44no—
76#208—124no—
77#208—124no—
78C2×C3⋊C8—64no—
79C2×C3⋊C8—64no—
80C22×C32—21no—
81C22×C32—22no—
82C22×C32—22no—
83C22×C32—22no—
84C22×C32—44no—
85C22×C32#9511yescharacteristic
86C22×C32#10414yes—
87C32×C4—21no—
88C32×C4—22no—
89C32×C4#9912yes—
90C3×Dic3—48no—
91C23×C4D3211yescharacteristic
92C2×M16—92no—
93C2×C22⋊C4—62no—
94C2×C42—62no—
95C22⋊C8—182no—
96#95—34no—
97C23×C3—24no—
98C23×C3—24no—
99C23×C3—22no—
100C23×C3—21no—
101C23×C3—44no—
102C23×C3—42no—
103C23×C3—42no—
104C23×C3Dic3⋊C412yes—
105C23×C3(C2×D3)⋊C412yes—
106C23×C3#21712yes—
107C2×C3×C4—24no—
108C2×C3×C4—24no—
109C2×C3×C4—24no—
110C2×C3×C4—24no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—22no—
114C2×C3×C4—44no—
115C2×C3×C4—42no—
116C2×C3×C4—42no—
117C2×C3×C4—42no—
118C2×C3×C4—44no—
119C2×C3×C4—42no—
120C2×C3×C4—68no—
121C2×C3×C4—124no—
122C2×C3×C4—124no—
123C2×C3×C4C4×Dic312yes—
124C2×C3×C4Dic3⋊C412yes—
125C2×C3×C4C4⋊Dic312yes—
126C2×C3×C4(C2×D3)⋊C412yes—
127C2×Dic3—28no—
128C2×Dic3—44no—
129C2×Dic3—44no—
130C3⋊C8—124no—
131C3⋊C8—124no—
132C2×C32—24no—
133C2×C32—41no—
134C2×C32#33912yes—
135C2×C32#34211yescharacteristic
136C24#62511yescharacteristic
137C22×C4—42no—
138C22×C4—64no—
139C22×C4D3×Dic312yes—
140C22×C4#62411yescharacteristic
141C22×C4#62612yes—
142C22×C4#62711yescharacteristic
143M16—362no—
144C2×C8—182no—
145C22⋊C4—68no—
146C42—124no—
147C22×C3—22no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—22no—
152C22×C3—22no—
153C22×C3—22no—
154C22×C3—22no—
155C22×C3—24no—
156C22×C3—21no—
157C22×C3—42no—
158C22×C3—42no—
159C22×C3—42no—
160C22×C3—48no—
161C22×C3—48no—
162C22×C3#80514yes—
163C22×C3C3⋊#9512yes—
164C22×C3#83714yes—
165C3×C4—22no—
166C3×C4—22no—
167C3×C4—22no—
168C3×C4—22no—
169C3×C4—22no—
170C3×C4—42no—
171C3×C4—128no—
172C3×C4#80614yes—
173Dic3—48no—
174C32#129711yescharacteristic, complemented, Sylow
175C23—24no—
176C23—41no—
177C23(C2×D3)⋊Dic312yes—
178C23#372411yescharacteristic
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—41no—
183C2×C4—68no—
184C2×C4—124no—
185C2×C4—124no—
186C2×C4Dic3211yescharacteristic
187C2×C4#372211yescharacteristic
188C2×C4Dic3⋊Dic312yes—
189C8—362no—
190C2×C3—24no—
191C2×C3—24no—
192C2×C3—21no—
193C2×C3—22no—
194C2×C3—44no—
195C2×C3—42no—
196C2×C3—42no—
197C2×C3#452312yes—
198C2×C3#452712yes—
199C2×C3#453212yes—
200C22—22no—
201C22—22no—
202C22—21no—
203C22—22no—
204C22—44no—
205C22#6356914yes—
206C22#6357911yescharacteristic
207C4—21no—
208C4—22no—
209C4—128no—
210C4#6358112yes—
211C3—21no—
212C3#6761812yescomplemented
213C2—24no—
214C2—41no—
215C2#1058916112yes—
216C2#1058918711yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32D4
hypocenterC32#1297
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. C2×#3748C4semidirect
9. C3×C3⋊#95C4semidirect
35. C3⋊#95Dic3semidirect
174. C32#1297semidirect
212. C3#67618semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105929062
C3×C4×#2172
#676183